Choice of wavelengths for multiwavelength optical imaging

ABSTRACT

The present invention relates to a method for wavelength selection in a multi-wavelength TPSF or CW-based optical imaging system. This consists of identifying several chromophores in a highly turbid medium and selecting optimized wavelengths whereby using these wavelengths optimizes the deduction of the chromophore concentrations. Such chromophore concentrations may be combined to deduce other properties of the turbid medium.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-In-Part Application ofPCT/CA02/01081, filed Jul. 16, 2002, designating the United States, nowpending. This application is also a Continuation-In-Part of U.S. patentapplication Ser. No. 09/985,436, filed Nov. 2, 2001, now U.S. Pat. No.6,694,159 now pending. This application claims priority under 35 U.S.C.119(e) of U.S. Provisional Patent Application Ser. No. 60/305,092 filedJul. 16, 2001. This application is also a Continuation in part ofPCT/CA03/00046, filed Jan. 22, 2003, designating the United States, nowpending. The specifications of said applications are hereby incorporatedby reference.

MICROFICHE APPENDIX

Not applicable.

FIELD OF THE INVENTION

The present invention relates to the field of optical imaging in whichobjects which diffuse light, such as some human body tissues, are imagedusing signals resulting from the injection of light into the object anddetection of the diffusion of the light in the object at a number ofpositions. More particularly, the present invention relates to thechoice of wavelengths for multiwavelength optical imaging in order toprovide enhanced information.

BACKGROUND OF THE INVENTION

Optical medical imaging modalities such as Time-Domain and ContinuousWave show great promise as techniques for imaging breast tissue, as wellas the brain and other body parts. In TD, the objective is to analyzethe temporal point spread function (TPSF) of an injected pulse of lightas it is diffused in the tissue. With CW, the attenuation of acontinuous light source is measured. The information extracted from theTPSF and the attenuation signal is used in constructing medically usefulimages.

For example, one can extract time-gated attenuation information from theTPSF which provides high quality images albeit of lower resolution thanother modalities such as X-ray imaging. Thus, it is unclear whether thespatial resolution provided by optical imaging is adeuate for diagnosingbreast cancer based on morphology.

CW and TPSF data, when processed adequately, can be used to extractabsorption values from raw measurements. For example, the TPSF can beused to decouple the light attenuation into absorption and scatteringcomponents. This extra information may be clinically useful. Moreover,one can obtain the tissue absorption spectrum by performing time-domainmeasurements at multiple wavelengths. In tissue there are severalmolecules which absorb the light and are known as chromophores.Spectroscopic analysis of the tissue absorption spectrum permitschromophore concentrations to be measured. Furthermore, combination ofthe chromophore concentrations can yield physiological information, asopposed to morphologic information, which could provide a more medicallyuseful image.

The problem is one of knowing which are the dominant chromophores toinclude in a tissue model and then choosing the “best” wavelengths todeduce their concentrations most accurately.

SUMMARY OF THE INVENTION

It is an object of the invention to improve image quality in TPSF orCW-based optical images by choosing an efficient combination ofwavelengths and combining information from the combination ofwavelengths.

It is an object of the present invention to provide an objective methodfor choosing the wavelengths for a multiwavelength TPSF or CW-basedoptical imaging approach. For a given set of chromophores, the bestselection of the wavelengths is performed for the set as a whole asopposed to choosing the best wavelength for each chromophoreindividually. Furthermore, hardware constraints can be taken intoconsideration in order to optimize the selection of wavelengths for agiven device.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 illustrates the absorption spectra used of oxy-Hb, deoxy-Hb, purewater and lipid;

FIG. 2 illustrates the inverse of the condition number of the hemoglobinspecific absorption matrix as a function of wavelength λ1 being plottedfor a system of a) two wavelengths. where the other wavelength is fixedat λ2=850 nm, b) three wavelengths where the other wavelengths are fixedλ2=850 nm and λ3=758 nm and c) four wavelengths where the otherwavelengths are fixed λ2=850 nm, λ3=758 nm and λ4=800 nm;

FIG. 3 illustrates the inverse of condition number C for the specificabsorption spectra of oxy-Hb and deoxy-Hb as a function of λ1 and λ2.The plot is symmetric with respect to the diagonal. Regions of highvalues indicate combinations of wavelengths advantageous forspectroscopy;

FIG. 4 illustrates the deviation of calculated saturation and truesaturation (S(calc)−S(true)) for a model tissue containing 15 μM [HbT],S(true)=25%, 50% and 75% and a lipid concentration of 40%. Twowavelengths at 760 and 850 nm were used to fit [oxy-Hb] and [deoxy-Hb].The sensitivity with respect to wrong assumptions of lipid and waterconcentrations are shown;

FIG. 5A illustrates the inverse of condition number C for the specificabsorption spectra of oxy-Hb and deoxy-Hb and lipid for a fixedwavelength λ3=830 nm as a function of λ1 and λ2. The islands of highvalues indicate advantageous wavelengths (scaling 0-0.01);

FIG. 5B illustrates the inverse of condition number C for the specificabsorption spectra of oxy-Hb and deoxy-Hb and lipid for a fixedwavelength λ3=830 nm as a function of λ1 and λ2 (same as FIG. 5A butscaling 0-0.0005);

FIG. 6A illustrates the inverse of condition number C for the specificabsorption spectra of oxy-Hb and deoxy-Hb, lipid and water for two fixedwavelength at λ3=760 nm and λ4=830 nm as function of λ1 and λ2 (scaling0-0.0015). Regions of high values are advantageous for spectroscopy;

FIG. 6B illustrates the inverse of condition number C for the specificabsorption spectra of oxy-Hb and deoxy-Hb, lipid and water for two fixedwavelength at λ3=760 nm and λ4=830 nm as function of λ1 and λ2. (same asFIG. 6A but scaling 0-0.0005);

FIG. 7 illustrates the estimation of deviations from true saturationvalues for a model tissue of [HbT]=20 μM, S=75%, a lipid concentrationof 40% and true water concentration corresponding to 0-100% water. Threewavelengths at 760, 780 and 850 nm were used for back calculation of S,shown here as a function of assumed water concentration;

FIG. 8 illustrates the estimation of the influence of errors (noise) inμ_(a) on the calculated Hb concentrations and saturation values. A modelμ_(a)-spectrum based on 20 μM [HbT], S=50%, and a lipid and waterconcentration of 30% and 40% was assumed. Matrix inversion was performedfor wavelengths 760, 790, 830 and 850 nm. plotted is the change incalculated [oxy-Hb], [deoxy-Hb] and saturation value when the μ_(a)value at a single wavelength was changed by +0.0001 mm⁻¹. This plotsuggests that noise at 830 nm translates in the highest noise insaturation values;

FIG. 9 illustrates the estimation of the recovery of saturation valuesbased on different wavelength combinations. A model tissue of 20 μM[HbT], a true saturation of S=75%, lipid and water concentration of 40%were used. in the lower plot an offset of 0.0005 mm⁻¹ independent ofwavelength was added to the model tissue μa-spectrum (no offset in theupper plot). Plotted are deviations of the saturation values due tomatrix inversion and the true 75% value. The following wavelengthcombinations were used: 1) 760 nm and 850 nm, 2) 760, 830 and 850 nm, 3)760, 780, 830 and 850 nm, 4) 750-850nm, 5) 720-850 nm, 6) 720-900 nm;and

FIG. 10 illustrates the estimation of the recovery of saturation valuesbased on different wavelength combinations. A model tissue of 20 μM[HbT], a true saturation of S=50%, lipid and water concentration of 40%were used in the lower plot an offset of 0.0005 mm⁻¹ independent ofwavelength was added to the model tissue μa-spectrum (no offset in theupper plot). Plotted are deviations of the saturation values due tomatrix inversion and the true 75% value. The following wavelengthcombinations were used: 1) 760 nm and 850 nm, 2) 760, 830 and 850 nm, 3)760, 780, 830 and 850 nm, 4) 750-850 nm, 5) 720-850 nm, 6) 720-900 nm.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION OF THE INVENTION

In accordance with the present invention, there is provided a method forselecting wavelengths for multiwavelength optical imaging.

Tissue Chromophores

The dominant near infrared chromophores contained in breast tissue areconsidered to be hemoglobin (Hb) in its oxygenated (oxy-Hb) anddeoxygenated (deoxy-Hb) forms, water and lipids. FIG. 1 shows theabsorption spectra of oxy-Hb (at 10 μM concentration), deoxy-Hb (at 10μM concentration), pure water (100% concentration), lipid (absorptionspectrum of olive oil has been used to estimate the absorption spectrumof fat). There are other interesting near infrared chromophores, such asglucose and cytochrome c oxidase, but their absorption contribution inthe breast is considered negligible compared to the aforementionedchromophores.

Physiological Information

Potentially useful physiological information about the breast tissue canbe obtained from concentrations,[ ], of the chromophores. The totalhemoglobin concentration, [HbT], defined as [HbT]=[oxy-Hb]+[deoxy-Hb],is related to the local vascular density. Since cancer is commonlyassociated with an increase in vascularisation (angiogenesis), ameasurement of [HbT] could be medically useful. The fraction ofhemoglobin that binds to oxygen is known as the oxygen saturation, S,and defined as S=[oxy-Hb]/[HbT]. Increased metabolic activity increasesoxygen demands which decreases the oxygen saturation. Since cancer iscommonly associated with increased metabolic activity, a measurement ofS could also be medically useful.

Wavelength Choice

Historically as the biomedical optics field evolved the wavelengths werechosen for each chromophore individually by observing strong nearinfrared spectral features for the given chromophore and using theclosest hardware-available wavelength. Many researchers also used theisobestic wavelength of oxy-Hb and deoxy-Hb, the wavelength where theirabsorption per concentration are equal, since this wavelength isinsensitive to the oxygenation state of the hemoglobin and can berelated to the (HbT).

However, the question both posed and addressed here is that for a givenset of chromophores what are the optimal wavelengths to use in order todeduce the concentration of each chromophore? It is interesting to notethat the isobestic wavelength used by many researchers turns out not tobe one of the wavelengths of choice.

It is an object of the present invention to provide an objective methodfor choosing the wavelengths for a multiwavelength TPSF or CW-basedoptical imaging approach. For a given set of chromophores, the bestselection of the wavelengths is performed for the set as a whole asopposed to choosing the best wavelength for each chromophoreindividually. Moreover, it is also possible to investigate scenariossuch as the influence on determining chromophore concentrations undercertain assumptions about the concentrations of other chromophore(s) inthe set. Furthermore, hardware constraints can also be taken intoconsideration in order to optimize the selection of wavelengths for agiven device. Fortunately, the recent advent of turn-key, pulsed,tunable near infrared wavelength lasers has permitted more viableavailability of near infrared wavelengths.

Experimental Brute Force Approach

One possible approach to optimize the choice of wavelengths for a givenset of chromophores is to conduct a brute force experimental study. Thiswould consist of performing numerous experiments where differentcombinations of wavelengths are evaluated for the given set ofchromophores at known concentrations until the optimum combination fordeducing their concentrations is found. Obviously, this approach islikely to be highly time-consuming and it is not always trivial toprovide a set of chromophores at known concentrations, particularly inthe case of in vivo breast tissue.

Matrix Inversion Sensitivity Approach

An alternative approach which avoids the numerous experiments of theexperimental brute force approach is a matrix inversion sensitivityapproach. While the following example of an embodiment of the inventionwill be described with reference to TPSF-based parameters, it will beappreciated that by those skilled in the art that the example can beadapted to CW parameters as will be further explained below.

The equation which needs to be solved can be written for each wavelengthas:

$\begin{matrix}{{\mu_{a}\left( \lambda_{1} \right)} = {\sum\limits_{i}{{m_{a,i}\left( \lambda_{1} \right)} \cdot c_{i}}}} \\{{\mu_{a}\left( \lambda_{2} \right)} = {\sum\limits_{i}{{m_{a,i}\left( \lambda_{2} \right)} \cdot c_{i}}}} \\\ldots \\{{\mu_{a}\left( \lambda_{3} \right)} = {\sum\limits_{i}{{m_{a,i}\left( \lambda_{3} \right)} \cdot c_{i}}}}\end{matrix}$where μa is the measured absorption coefficient, ma is the specificabsorption coefficient of the different chromophores and ci is thecorresponding concentration.

This is written is matrix form as:μ_(a) =M·cwhere printing in bold indicates a matrix or vector. μ_(a) is a vectorwith a number of rows corresponding to the number of wavelengths(n_(λ)). c is a vector with the number of rows corresponding to thenumber of chromophores (n_(c)). M is a rectangular matrix of sizen_(λ)×n_(c).

If n_(λ)=n_(c) the system can be solved by matrix inversion c=M⁻¹μ_(a)and if n_(λ)>n_(c) the system is overdetermined and can be solved by thepseudo-inverse M⁺=(M^(T)M)⁻¹M^(T) where M^(T) is the transposed matrixof M.c=(M ⁺)μ_(a)

The pseudoinverse M⁺ is an n_(λ)×n_(c) array which is unique. If M issquare (i.e. not overdetermined) the M⁺=M⁻¹. For given (i.e. chosen)wavelengths the pseudoinverse M⁺ can be precalculated once and thematrix inversion corresponds to a simple matrix multiplication. This isthe basis for the calculation of chromophore concentration.

One means to quantify the expected sensitivity of a matrix inversion ofa matrix M with respect to small errors in the data is the conditionnumber C which is defined as:C=norm(M)·norm(M ⁻¹)

C gives an indication of the accuracy of the results and is an estimateof the cross-talk between the different channels (i.e. chromophoresconcentrations). Values of C near 1 indicate a well-conditioned matrix,large values indicate an ill-conditioned matrix. The condition number isclosely related to singular value decomposition (SVD) as it is the ratioof the largest and the smallest singular value of a matrix.

The matrix M for oxy-Hb and deoxy-HB at λ=760 and 770 nm is

$M = \begin{matrix}0.3871 & {{0.1465\mspace{11mu}\lambda} = {760\mspace{11mu}{nm}}} \\0.3280 & {{0.1625\mspace{11mu}\lambda} = {770\mspace{11mu}{nm}}}\end{matrix}$

A matrix inversion is possible as the rank (M)=2, however the absorptionat the two wavelengths is ‘similar’. The condition number is C=20.49.Choosing the wavelengths to be λ=760 and 850 nm gives the matrix

$M = \begin{matrix}0.3871 & 0.1465 \\0.1729 & 0.2645\end{matrix}$

Inspection by eye already shows that the absorption is very ‘different’.This is confirmed by the condition number: C=3.206. In what followsbelow the inverse of the condition number is plotted and analyzed. Ithas value between 0 and 1. 1/C close to 1 means ‘orthogonal’ spectra andlow sensitivity to cross-talk. Small values of 1/C mean anill-conditioned matrix. To find the best wavelengths, 1/C is calculatedas a function of a wavelength. The wavelengths that give the highestvalues of 1/C are the best for a calculation of chromophoreconcentrations and the subsequent physiological information such asoxygen saturation, S.

Model absorption spectra were generated with the absorption spectra ofFIG. 1 based on estimations of [HbT], S, lipid and water concentration.Matrix inversion based on different sets of wavelengths were performedto recover these parameters. These parameters were compared with thetrue ones for the different wavelengths and the sensitivity to noise ormeasurement offsets considered.

Assuming that we fit for the hemoglobin concentrations only and assumingcertain values for water and lipid concentration, for a x-wavelengthsmatrix inversion, the best combination of wavelengths to give awell-conditioned matrix, the sensitivity of calculated values of oxy-Hband deoxy-Hb concentration and oxygen saturation for variations of lipidor water concentration and sensitivity of S to measurement noise havebeen determined.

In FIG. 2 the inverse of the condition number is shown for matrices ofoxy-Hb and deoxy-Hb specific absorption coefficients for 2, 3 and 4wavelengths. In each case one wavelength (λ₁) was varied between 650 and950 nm while the remaining wavelengths were fixed λ₂=850 nm(2-wavelength system) λ₂=850 nm and λ₃=758 nm (3-wavelength system), andλ₂=850 nm, λ₃=758 nm and λ₄=800 nm (4-wavelength system). FIG. 2indicates that the selection of two wavelength at λ₁=850 nm and λ₂=700nm gives the highest values of 1/C and when the wavelength range isrestricted via hardware constraints to >750 nm, a system that includesthe peak wavelength of deoxy-Hb close to 760 nm is advantageous. It doesnot matter whether two or more wavelengths are used. This somewhatcounterintuitive result is valid only without measurement noise andnoise in the background absorption.

FIG. 3 further highlights this finding for a two-wavelength matrixinversion. In this figure 1/C is plotted as a function of both at λ₁ andλ₂ in the range 650-950 nm. The plot is symmetric with respect to thediagonal. Regions of high 1/C-values can be chosen and the corresponding‘good’ wavelengths can be read off the axis. It is apparent that (withthe restriction to >750 nm) the one wavelength should be close to 760 nmwhile the other one can be within the range 830-900 nm withoutsubstantially affecting the condition number.

Using the spectra shown in FIG. 1, model tissue absorption spectra weregenerated. Based on matrix inversion values of [oxy-Hb], [deoxy-Hb] andS were backcalculated and the sensitivity to incorrect assumptions aboutthe [water] and [lipid] tested. One approach is to take the measuredμ_(a) spectra and subtract water and lipid absorption corresponding tocertain assumed concentrations. For the data shown in FIG. 4, a modeltissue containing 15 μM [HbT] , (true) saturation values of S=25%, 50%and 75% was used. Lipid concentration was 40%. It was tested how amisjudgement of water concentration affects the recalculated S value. Totest the error in a simple two-wavelengths-fit (760 and 850 nm), theassumed lipid concentration was varied between 0 and 100%. When theassumed water concentration is right (lower three lines in FIG. 4), thedeviation in saturation between true and calculated values is <±2%(obviously with zero error for the right lipid concentration of 40%). Amisjudgement about the water concentration by 20% (upper lines in FIG.5) results in additional errors in S(calc)−S(true) of up to 2% forS=75%, 4% for S=50% and 8% for S=25%. These errors in S are a functionof the underlying tissue absorption coefficients. The values here givean indication about the order of magnitude.

Having a system with more than two fit-parameters, best wavelengthcombinations, for a three-components system of oxy-Hb, deoxy-Hb andlipid system, for a four-components system of oxy-Hb, deoxy-Hb, lipidand water, and the sensitivity of calculation of S to noise at thedifferent wavelengths have been determined.

In FIGS. 5A and 5B the inverse of the condition number is plotted for athree wavelengths system based on the oxy-Hb, deoxy-Hb and lipidspecific absorption spectra as a function of λ₁ and λ₂. The thirdwavelength was fixed at λ3=830 nm. Again, the plot is symmetric withrespect to the diagonal. From FIG. 5A it is apparent, that there arethree “islands” of high 1/C values. Unfortunately, all of these islandwould include wavelengths outside an imposed hardware constrainedwavelength range of 750 to 850 nm. Plotting the same data in a differentscale (FIG. 5B) shows that there is just a single preferentialcombination within this hardware constrained wavelength range: 760 and780 nm.

Equivalent to FIGS. 5A and 5B, the inverse of C for a 4-wavelengthssystem is plotted in FIGS. 6A and 6B. Again, the difference between themis the scaling. Two wavelengths were fixed at λ3=760 nm and λ4=830 nm.Including the wavelengths outside the 750-850 nm range there appear fourpreferential combinations. Restricting the wavelength range to 750-850nm there are just two advantageous region (marked by the white rectanglein FIG. 6B): 780 nm and 850 nm, and 780 nm and 815 nm.

From the analysis based on matrix condition numbers, the best wavelengthcombinations for 2, 3 and 4 wavelengths measurements are the following:

TABLE 1 Wavelength combinations for 2, 3 and 4 wavelengths measurementsWavelength Best wavelengths (nm) see Range λ1 λ2 λ3 λ4 fit for FIG. 2-λ650–950 nm 700 >860  Oxy-Hb, 2, 3 750–850 nm 760 850 deoxy-Hb 3-λ650–950 nm  700– 830 925 +lipid 5A, 760 830  860– 925 B 870 750–850 nm760 780 830 4-λ 650–950 nm 760 830 860 925 +lipid, 6A, 700 760 830 925+water B 750–850 nm 760 780 830 850 Best 760 780 815 830 combination

Furthermore, it must be pointed out that including more wavelengths doesnot increase the condition number. E.g. for the four chromophores andall wavelengths in the range 750-850 nm, 1/C=0.000314. This is lowerthan the value (1/C=0.00036, compare with FIG. 6B) when only fourwavelengths (760, 760, 830 and 850 nm) are used. In a system withoutnoise and no other chromophores than the four considered here, a4-wavelengths system is the optimal.

While certainly only a 4-wavelengths measurement allows [oxy-Hb],[deoxy-Hb], [lipid] and [water] to be determined, and a 2-wavelengthssystem (see FIG. 5) is not sufficient, the question is posed whether a3-wavelengths measurement might supply S values with a high enoughprecision. In this case the concentration of one chromophore (water orlipid) must be guessed and the corresponding absorption subtracted fromthe measured μ_(a) values. This was tested with a model absorptionspectrum and is shown in FIG. 7 for 760, 780 and 850 nm. True waterconcentration was varied between 10 and 100% (the different lines), andthe difference between calculated and true saturation values plotted asa function of assumed water concentration. For instance, for a truewater concentration of 50%, a misjudgment of the water concentration by10% results in an error in S by about 4%.

Up to now, only “perfect” data sets were considered with no noise. Inreal situations there are problems due to measurement noise that israndom for the different wavelengths; unknown chromophores in thetissue, i.e. there is a background absorption coefficient the spectrumof which we do not know; and possible systematic errors in the primaryμ_(a) recovery.

There are an ample number of parameters which can be considered and asexamples the following two questions are considered. First, is theoxygen saturation more susceptible to noise at certain wavelengths?Second, what is the influence of an offset in the μ_(a) data?

The influence of errors (noise) in μ_(a) on the calculated Hbconcentrations and saturation values was estimated in a model tissuebased on 20 μM [HbT], S=50% and a lipid and water concentration of 30%and 40% respectively. Matrix inversion was performed on theμ_(a)-spectrum of this model tissue for wavelengths 760, 780, 830 and850 nm. The sensitivity to noise (i.e. variations in μa) at thedifferent wavelengths was estimated by changing the absorptioncoefficient at a single wavelength by +0.0001 mm⁻¹. In FIG. 3, thechange in calculated (oxy-Hb), [deoxy-Hb] and oxygen saturation valuedue to this “noise” is plotted. This figure shows that the change inoxygen saturation value is about −2% for changes at 760 nm, <0.5% at 780nm, while it translates to a variation of +6% at 830 nm.

There are two conditions that produce an offset in the measuredμ_(s)-spectra with respect to the true values. First, the algorithm forμ_(a)-calculation based on TPSF-based optical imaging might lead to asystematic offset e.g. due to residual crosstalk between absorption andscattering parameters. Second, the tissue absorption might have abackground of unknown origin (chromophore). Under both conditions thefitting of μ_(a)-data with the four chromophores is hampered. The effectof such an offset for different wavelength combinations is estimatedwith a model spectrum of 20 μM (HbT), S=75% and water and lipidconcentration of 40%. An offset of 0.0005 mm⁻¹ was added to theμ_(a)-values independent of wavelength. The effect on the calculatedoxygen saturation values is known in FIG. 9 for combination of 2, 3 and4 wavelengths as well as continuous spectra between 750-850, 720-850 and720-900 nm. It is apparent that the lowest error in S is achieved by the4-wavelengths combination. Including more wavelengths increases theerror. In FIG. 10 the same calculation was done, however, for a trueoxygen saturation value of 50%. Here the lowest error is achieved by the720-850 nm wavelength range, while using less wavelengths or increasingthe fitting range to 900 nm results in larger errors.

Based on the assumption that the dominant tissue chromophores areoxy-Hb, deoxy-Hb, water and lipid and analysis of the matrix conditionnumber, measurements at the wavelengths 760, 780, 830 and 850 nm supplyan optimal data set when the wavelength range is limited to 750-850 nmunder ideal conditions. As shown in FIGS. 5 and 6, inclusion of shorterand longer wavelengths promise a better matrix inversion. Under realconditions there is no clear-cut answer about the improvement when morewavelengths are included (see FIGS. 9 and 10). It might be advantageousto reduce measurement noise at 4 wavelengths due to longer scan timesrather than to include more wavelengths. As demonstrated in FIG. 8, toachieve an optimal accuracy the noise level at different wavelengths hasto be adjusted which might require different measurement times atcertain wavelengths.

Strictly speaking the work presented here was achieved by optimizing a2-wavelength system and then optimizing a 4-wavelength system where 2 ofthe wavelengths were fixed at the optimized 2-wavelength system values.Whilst this is easier to display graphically, preferably all 4wavelengths would be permitted to vary in a global optimization process.Fortunately, for the specific example presented here when all 4wavelengths are permitted to vary the same optimal solution is found.However, this may not be true for all situations and a globaloptimization is preferred.

It will be appreciated that parameters of the system other thanwavelengths can be optimized For example the light source type andsource power, the detector type and detector aperture for eachwavelengths, the choice of image algorithm, the source/detectorgeometries, the acquisition time and the noise characteristics areparameters that can be adjusted or chosen, as would be known to oneskilled in the art, to optimize the determination of chromophoresconcentration and the optical image obtained therewith. In a preferredembodiment, optimization of the parameters is performed by taking inconsideration the matrix inversion approach for optimizing wavelengthselection as described above.

It is also understood that it will be obvious to those skilled in theart that the same approach for choosing optimal wavelengths can beapplied to optical absorption spectroscopy in general. For example, inother embodiments of the present invention the method of the presentinvention is also used for choosing the optimal wavelengths foranalyzing the components of paints, pharmaceutical products, food, grainor any other turbid media.

It is also understood that the proposed method applies both to theanalysis of absolute chromophore concentrations as to their changes orrelative concentrations.

It is also understood that the proposed method applies both to theanalysis of absolute chromophore concentrations as to their changes orrelative concentrations.

Further, it is also understood that the proposed method applies whencontinuous wave (CW) methods are used and an assumption for scatteringis made, e.g. a constant value or following a scatter-power wavelengthdependent law, in order to infer the absorption coefficient, rather thanmeasuring the absorption coefficient directly with a TPSF-basedapproach.

Thus, changes in CW measurements can be converted into absorptionchanges ΔA(λ) which are then used to calculate changes in concentrationsΔc_(i) based on a modified Beer-Lambert law which assumes apredetermined wavelength dependence of the optical pathlength D₉(λ)(Cope & Delpy, 1998; Essenpreis et al., 1992) to account for scattering.

${\Delta\;{A(\lambda)}} = {\sum\limits_{i}\left\lbrack {{{m_{ai}(\lambda)} \cdot \Delta}\;{c_{i} \cdot {D_{a}(\lambda)}}} \right\rbrack}$

Thus Δc_(i)=N⁻¹ΔA, where N is similar to M but incorporates D₉(λ), andis the matrix which is used for optimizing the choice of wavelengths.

Further, it is understood that the proposed method applies not only fora mixture of endogenous absorbers (chromophores), but also for mixturesof exogenous absorbers with known spectra, such as optical dyes orfluorophores, or for a mixture of both endogenous and exogenousabsorbers.

While the invention has been described in connection with specificembodiments thereof, it will be understood that it is capable of furthermodifications and this application is intended to cover any variations,uses, or adaptations of the invention following, in general, theprinciples of the invention and including such departures from thepresent disclosures as come within known or customary practice withinthe art to which the invention pertains and as may be applied to theessential features herein before set forth, and as follows in the scopeof the appended claims.

The embodiment (s) of the invention described above is(are) intended tobe exemplary only. The scope of the invention is therefore intended tobe limited solely by the scope of the appended claims.

1. A method of optical imaging of turbid media using a plurality ofdiscrete wavelengths in an optical imaging system, the method comprisingthe steps of: selecting a set of chromophores for characterizing aproperty of the turbid media; defining parameters of the systemincluding at least a number of said discrete wavelengths, a value ofeach of said wavelengths, source power and detector aperture for each ofsaid wavelengths, a choice of image algorithm and source/detectorgeometries, a choice of source and detector and noise characteristics;fixing a value of all of said parameters except a plurality of saidparameters values to be optimized; determining an optimal value for eachof said parameter values to be optimized as a function of a performanceof the system in measuring a concentration of said chromophores in saidturbid media for characterizing said property as a whole; and using saidoptimal value for each of said parameter values in imaging said turbidmedia.
 2. The method of claim 1 wherein said optical imaging system isselected from Time-Domain (TD) modality which generates Temporal PointSpread Functions (TPSF), and Continuous Wave (CW) modality.
 3. Themethod of claim 2, wherein said imaging is medical imaging, said highlyturbid medium being body tissue and said property is physiological. 4.The method of claim 3, wherein said parameter values to be optimizedcomprise a value of each of said wavelengths.
 5. The method of claim 4,wherein said parameter values to be optimized further comprise saidnumber of said discrete wavelengths.
 6. The method of claim 5, whereinsaid step of determining comprises fixing said number of discretewavelengths at each of a plurality of numbers, and determining anoptimized performance of the system in measuring a concentration of saidchromophores in said turbid media at each of said plurality ofwavelengths, and selecting one of said plurality of numbers having abest optimized performance.
 7. The method of claim 6, wherein said stepof determining an optimal value for each of said parameters comprisesminimizing a condition number of a matrix of specific absorptioncoefficients of said chromophores as a function of wavelength.
 8. Themethod of claim 5, wherein said step of determining an optimal value foreach of said parameters comprises minimizing a condition number of amatrix of specific absorption coefficients of said chromophores as afunction of wavelength.
 9. The method of claim 4, wherein said step ofdetermining an optimal value for each of said parameters comprisesminimizing a condition number of a matrix of specific absorptioncoefficients of said chromophores as a function of wavelength.
 10. Themethod of claim 3, wherein said plurality of chromophores comprise atleast oxy-hemoglobin and deoxy-hemoglobin.
 11. The method of claim 10,wherein said chromophores are water, lipids, oxy-hemoglobin anddeoxy-hemoglobin.
 12. The method of claim 11, wherein said imagingsystem is TPSF-based and wherein values of said wavelengths are 760 nm,780 nm, 830 nm and 850 nm.
 13. The method of claim 10, wherein said bodytissue is breast tissue.
 14. The method of claim 10, wherein saidoptical imaging system is TPSF-based and wherein said number ofwavelengths selected is from 2 to
 4. 15. The method of claim 14, whereinsaid number is
 4. 16. The method of claim 1, wherein said step ofdetermining comprises empirically determining said performance of thesystem for a range of said values for each of said parameter values tobe optimized.
 17. The method of claim 1, wherein the step of determiningan optimal value of said parameters to be optimized comprises: derivingan inherent wavelength-dependent sensitivity to noise in calculatingsaid chromophore concentrations, and determining an optimal correlationof said sensitivity and at least one other of said parameters.
 18. Themethod of claim 17, wherein said imaging system is TPSF-based andwherein one of said parameters to be optimized is a distribution of anacquisition time at each of said wavelengths.
 19. The method of claim 1,wherein said imaging system is TPSF-based and wherein one of saidparameters to be optimized is a distribution of an acquisition time ateach of said wavelengths.
 20. The method of claim 19, further comprisinga step of determining a minimum value for said acquisition time at whichsaid performance of said system attains a minimum threshold value. 21.The method of claim 1, wherein one of said parameters to be optimized isat least one of said source power and said detector aperture for each ofsaid wavelengths.
 22. The method of claim 21 wherein said imaging systemis TPSF-based, further comprising a step of determining a minimum valuefor an acquisition time at which said performance of said system attainsa minimum threshold value.